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**1. Homework Statement**

A 100-turn, 2.0-cm-diameter coil is at rest in a horizontal plane. A uniform magnetic field away from vertical increases from 0.50 T to 1.50 T in 0.60 s. What is the induced emf (in mV) in the coil?

**2. Homework Equations**

[tex]\Phi_m = ABcos\vartheta[/tex]

[tex]E = \frac{d \Phi}{dt}[/tex]

**3. The Attempt at a Solution**

[tex]E = \frac{d \Phi}{dt} = \frac{d (ABcos\vartheta)}{dt} = - \pi r^2 \frac{dB}{dt}sin\vartheta[/tex]

[tex]\frac{dB}{dt} = \frac{1}{.6} = 1.67 T[/tex]

I can "ignore" the negative sign because I just need the absolute value, and the derivative of cos = -sin

*I forgot the number ot turns in the previous equation, but I added them in the next one*

[tex]N \pi r^2 \frac{dB}{dt}sin\vartheta = (100) \pi 0.1^2 (1.67) sin60 = 45mV[/tex]

Did I make any mistakes?